- #1

quietrain

- 655

- 2

## Homework Statement

find limit of

x

^{1/3}y

^{2}/ x + y

^{3}

as x,y tends to 0,0

## The Attempt at a Solution

i realise i can't use limits of individual variable since the denominator goes to 0 if x,y goes to 0,0

i realise i can't use squeeze theorem since the demnominator is not square, so negative numbers come into play

i realise that if i do a substitution of z = x

^{1/3}

i get

zy

^{2}/ z

^{3}+y

^{3}

which seems to be what the question is hinting... but i get stuck... anyone can help? thanks!

## Homework Statement

the next problem is to find all points that are continuous in the function f

f(x,y) = (y-5)cos(1/x

^{2}) if x not = 0

if x = 0, then f(x,y) = 0

## The Attempt at a Solution

my notes says that to show continuity, i must show that f(x,y) = f(a,b) when x,y tends to a,b

how do i do that?

does it mean i do something like this

-1< cos(1/x

^{2}) <1

(y-5) < (y-5)cos( 1/x

^{2}) < (y-5)

so all points are continuous except at x = 0 ?

BUt for f(x,y) = 0 when x = 0, it is not continous right? since cos(1/0) = undefined?

so the function is continous at all points except x= 0?

thanks!